Problem: 3 people can paint 6 walls in 50 minutes. How many minutes will it take for 4 people to paint 9 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 6\text{ walls}\\ p &= 3\text{ people}\\ t &= 50\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{6}{50 \cdot 3} = \dfrac{1}{25}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 4 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{1}{25} \cdot 4} = \dfrac{9}{\dfrac{4}{25}} = \dfrac{225}{4}\text{ minutes}$ $= 56 \dfrac{1}{4}\text{ minutes}$ Round to the nearest minute: $t = 56\text{ minutes}$